Problem: Find the distance between the vertices of the hyperbola
\[\frac{x^2}{99} - \frac{y^2}{36} = 1.\]
Solution: We read that $a^2 = 99,$ so $a = \sqrt{99} = 3 \sqrt{11}.$  Therefore, the distance between the vertices is $2a = \boxed{6 \sqrt{11}}.$